What does Acts 21:36 mean?

Paul has faced plenty of persecution, and he's been arrested by local authorities (Acts 16:19–24). However, this is the first recorded time he's arrested by the Roman military. To prove he's a devout Jew, he planned to provide the sacrifices for four men completing a Nazirite vow. Before they can finish the ritual, Jews, likely from Ephesus, falsely accuse him of bringing a Gentile, Trophimus the Ephesian, into the temple.

The temple was set up with graduated areas of exclusivity. In the outer courtyard, everyone, including Gentile God-fearers, could worship God and learn from the rabbis under Solomon's Portico. It is this area that Jesus cleared out when the moneychangers and bird merchants filled the space such that Gentiles had no place to worship (Matthew 21:12). Every ceremonially clean Jew was allowed on the porch and the first room in the temple. Clean men were allowed in the area closer to the altar. Only priests could go inside with the lampstand and the dedicated bread. Once a year, a designated priest could enter the Holy of Holies; the ark of the covenant was no longer there, but they still offered incense (Luke 1:8–9).

It's unclear if Trophimus was a God-fearer before he met Christ, but he certainly isn't fully converted to Judaism. He is allowed in the courtyard, but not inside the temple proper. For a Gentile to go beyond the courtyard would be to violate the Mosaic law—and the desecration of any authorized religious structure violated the Roman law and was punishable by death. Presumably, this Roman law is why the Sanhedrin tried to accuse Jesus of threatening the temple (Matthew 26:61).

Jews had very limited capital punishment authorization. When the crowd killed Stephen, it was illegal, but they were able to do so because Stephen was a complete unknown (Acts 7:54–60). With Paul, the mob may think they'll be permitted to kill because he committed a capital offense according to the Roman law—or so they think. The tribune and his soldiers stop the mob and rescue Paul by arresting him. Within days, faced with the always-volatile situation in Jerusalem, an assassination plot, and Paul's status as a Roman citizen, the tribune will soon decide the entire situation is beyond his paygrade and send Paul to the governor.